Dynamic semantics is a framework in
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
and
natural language semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynamic semantics, knowing the meaning of a sentence means knowing "the change it brings about in the information state of anyone who accepts the news conveyed by it."
In dynamic semantics, sentences are mapped to functions called ''context change potentials'', which take an input context and return an output context. Dynamic semantics was originally developed by
Irene Heim
Irene Roswitha Heim (born in Munich, Germany, on October 30, 1954) is a linguist and a leading specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before moving to the Massachusetts Institute of Technology i ...
and
Hans Kamp
Johan Anthony Willem "Hans" Kamp (born 5 September 1940) is a Dutch philosopher and linguist, responsible for introducing discourse representation theory (DRT) in 1981.
Kamp was born in Den Burg. He received a Ph.D. in Philosophy from UCLA in 19 ...
in 1981 to model
anaphora, but has since been applied widely to phenomena including
presupposition
In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include ...
,
plurals
The plural (sometimes abbreviated pl., pl, or ), in many languages, is one of the values of the grammatical category of number. The plural of a noun typically denotes a quantity greater than the default quantity represented by that noun. This de ...
,
questions
A question is an utterance which serves as a request for information. Questions are sometimes distinguished from interrogatives, which are the grammar, grammatical forms typically used to express them. Rhetorical questions, for instance, are inte ...
,
discourse relation A discourse relation (also coherence relation or rhetorical relation) is a description of how two segments of discourse are logically and/or structurally connected to one another.
A widely upheld position is that in coherent discourse, every ind ...
s, and
modality
Modality may refer to:
Humanities
* Modality (theology), the organization and structure of the church, as distinct from sodality or parachurch organizations
* Modality (music), in music, the subject concerning certain diatonic scales
* Modalitie ...
.
Dynamics of anaphora
The first systems of dynamic semantics were the closely related ''File Change Semantics'' and ''
discourse representation theory
In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT inclu ...
'', developed simultaneously and independently by
Irene Heim
Irene Roswitha Heim (born in Munich, Germany, on October 30, 1954) is a linguist and a leading specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before moving to the Massachusetts Institute of Technology i ...
and
Hans Kamp
Johan Anthony Willem "Hans" Kamp (born 5 September 1940) is a Dutch philosopher and linguist, responsible for introducing discourse representation theory (DRT) in 1981.
Kamp was born in Den Burg. He received a Ph.D. in Philosophy from UCLA in 19 ...
. These systems were intended to capture
donkey anaphora
Donkey sentences are sentences that contain a pronoun with clear meaning (it is Bound variable pronoun, bound semantics, semantically) but whose syntax, syntactical role in the sentence poses challenges to Linguist, grammarians. Such sentences def ...
, which resists an elegant compositional treatment in classic approaches to semantics such as
Montague grammar __notoc__
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use ...
.
Donkey anaphora is exemplified by the infamous donkey sentences, first noticed by the medieval logician
Walter Burley
Walter Burley (or Burleigh; 1275 – 1344/45) was an English scholastic philosopher and logician with at least 50 works attributed to him. He studied under Thomas WiltonHarjeet Singh Gill, ''Signification in language and culture'', Indian Inst ...
and brought to modern attention by
Peter Geach
Peter Thomas Geach (29 March 1916 – 21 December 2013) was a British philosopher who was Professor of Logic at the University of Leeds. His areas of interest were philosophical logic, ethics, history of philosophy, philosophy of religion and t ...
.
::Donkey sentence (relative clause): Every farmer who owns a donkey beats it.
::Donkey sentence (conditional): If a farmer owns a donkey, he beats it.
To capture the empirically observed truth conditions of such sentences in
first order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
, one would need to translate the
indefinite noun phrase "a donkey" as a
universal quantifier
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other w ...
scoping over the variable corresponding to the pronoun "it".
:: FOL translation of donkey sentence: :
While this translation captures (or approximates) the truth conditions of the natural language sentences, its relationship to the syntactic form of the sentence is puzzling in two ways. First, indefinites in non-donkey contexts normally express
existential
Existentialism ( ) is a form of philosophical inquiry that explores the problem of human existence and centers on human thinking, feeling, and acting. Existentialist thinkers frequently explore issues related to the meaning, purpose, and value ...
rather than universal quantification. Second, the syntactic position of the donkey pronoun would not normally allow it to be
bound
Bound or bounds may refer to:
Mathematics
* Bound variable
* Upper and lower bounds, observed limits of mathematical functions
Physics
* Bound state, a particle that has a tendency to remain localized in one or more regions of space
Geography
*B ...
by the indefinite.
To explain these peculiarities, Heim and Kamp proposed that natural language indefinites are special in that they introduce a new ''discourse referent'' that remains available outside the syntactic scope of the operator that introduced it. To cash this idea out, they proposed their respective formal systems that capture donkey anaphora because they validate ''Egli's theorem'' and its corollary.
::Egli's theorem:
::Egli's corollary:
Update semantics
''Update semantics'' is a framework within dynamic semantics that was developed by
Frank Veltman
Frank or Franks may refer to:
People
* Frank (given name)
* Frank (surname)
* Franks (surname)
* Franks, a medieval Germanic people
* Frank, a term in the Muslim world for all western Europeans, particularly during the Crusades - see Farang
Curre ...
.
In update semantics, each formula
is mapped to a function
Intersective update was proposed by Robert Stalnaker in 1978 as a way of formalizing the speech act of assertion.
In Stalnaker's original system, a context (or ''context set'') is defined as a set of possible worlds representing the information in the common ground of a conversation. For instance, if
C = \ this represents a scenario where the information agreed upon by all participants in the conversation indicates that the actual world must be either
w,
v, or
u. If
![\varphi!.html" ;"title="varphi.html" ;"title="![\varphi">![\varphi!">varphi.html" ;"title="![\varphi">![\varphi!= \, then updating
C with
\varphi would return a new context
Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
= \. Thus, an assertion of
\varphi would be understood as an attempt to rule out the possibility that the actual world is
u .
From a formal perspective, intersective update can be taken as a recipe for lifting one's preferred static semantics to dynamic semantics. For instance, if we take classical propositional semantics as our starting point, this recipe delivers the following intersective update semantics.
* Intersective update semantics based on classical propositional logic:
#
C = \
#
C neg \varphi= C - Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
#
C varphi \land \psi= Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
\cap Cpsi
Psi, PSI or Ψ may refer to:
Alphabetic letters
* Psi (Greek) (Ψ, ψ), the 23rd letter of the Greek alphabet
* Psi (Cyrillic) (Ѱ, ѱ), letter of the early Cyrillic alphabet, adopted from Greek
Arts and entertainment
* "Psi" as an abbreviation ...
#
C varphi \lor \psi= Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
\cup Cpsi
Psi, PSI or Ψ may refer to:
Alphabetic letters
* Psi (Greek) (Ψ, ψ), the 23rd letter of the Greek alphabet
* Psi (Cyrillic) (Ѱ, ѱ), letter of the early Cyrillic alphabet, adopted from Greek
Arts and entertainment
* "Psi" as an abbreviation ...
The notion of intersectivity can be decomposed into the two properties known as ''eliminativity'' and ''distributivity''. Eliminativity says that an update can only ever remove worlds from the context—it can't add them. Distributivity says that updating
C with
\varphi is equivalent to updating each singleton subset of
C with
\varphi and then pooling the results.
* Eliminativity:
\varphi is ''eliminative'' iff
Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
\subseteq C for all contexts
C
* Distributivity:
\varphi is ''distributive'' iff
Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
= \bigcup\
Intersectivity amounts to the conjunction of these two properties, as proven by
Johan van Benthem.
The test semantics for modals
The framework of update semantics is more general than static semantics because it is not limited to intersective meanings. Nonintersective meanings are theoretically useful because they contribute different information depending on what information is already present in the context. For instance, if
\varphi is intersective, then it will update any input context with the exact same information, namely the information encoded by the proposition
![\varphi!.html"_;"title="varphi.html"_;"title="![\varphi">![\varphi!">varphi.html"_;"title="![\varphi">![\varphi!/math>._On_the_other_hand,_if__\varphi_is_nonintersective,_it_could_contribute___![\varphi!.html"_;"title="varphi.html"_;"title="![\varphi">![\varphi!">varphi.html"_;"title="![\varphi">![\varphi!/math>_when_it_updates_some_contexts,_but_some_completely_different_information_when_it_updates_other_contexts.
Many_natural_language_expressions_have_been_argued_to_have_nonintersective_meanings._The_nonintersectivity_of_epistemic_modals_can_be_seen_in_the_ ![\varphi!.html"_;"title="varphi.html"_;"title="![\varphi">![\varphi!">varphi.html"_;"title="![\varphi">![\varphi!/math>._On_the_other_hand,_if__\varphi_is_nonintersective,_it_could_contribute___![\varphi!.html"_;"title="varphi.html"_;"title="![\varphi">![\varphi!">varphi.html"_;"title="![\varphi">![\varphi!/math>_when_it_updates_some_contexts,_but_some_completely_different_information_when_it_updates_other_contexts.
Many_natural_language_expressions_have_been_argued_to_have_nonintersective_meanings._The_nonintersectivity_of_epistemic_modals_can_be_seen_in_the_felicity_(linguistics)">infelicity_of_''epistemic_contradictions''.
:Epistemic_contradiction:_#It's_raining_and_it_might_not_be_raining.
These_sentences_have_been_argued_to_be_bona_fide_logical_contradictions,_unlike_superficially_similar_examples_such_as_![\varphi!.html"_;"title="varphi.html"_;"title="![\varphi">![\varphi!">varphi.html"_;"title="![\varphi">![\varphi!/math>._On_the_other_hand,_if_
_\varphi_is_nonintersective,_it_could_contribute_
__![\varphi!.html"_;"title="varphi.html"_;"title="![\varphi">![\varphi!">varphi.html"_;"title="![\varphi">![\varphi!/math>_when_it_updates_some_contexts,_but_some_completely_different_information_when_it_updates_other_contexts.
Many_natural_language_expressions_have_been_argued_to_have_nonintersective_meanings._The_nonintersectivity_of_epistemic_modals_can_be_seen_in_the_felicity_(linguistics)">infelicity_of_''epistemic_contradictions''.
:Epistemic_contradiction:_#It's_raining_and_it_might_not_be_raining.
These_sentences_have_been_argued_to_be_bona_fide_logical_contradictions,_unlike_superficially_similar_examples_such_as_Moore's_paradox">Moore_sentences,_which_can_be_given_a_pragmatics_(linguistics).html" "title="Moore's_paradox.html" ;"title="felicity_(linguistics).html" ;"title="varphi">![\varphi!.html" ;"title="varphi.html" ;"title="![\varphi">![\varphi!">varphi.html" ;"title="![\varphi">![\varphi!/math>. On the other hand, if \varphi is nonintersective, it could contribute ![\varphi!.html" ;"title="varphi.html" ;"title="![\varphi">![\varphi!">varphi.html" ;"title="![\varphi">![\varphi!/math> when it updates some contexts, but some completely different information when it updates other contexts.
Many natural language expressions have been argued to have nonintersective meanings. The nonintersectivity of epistemic modals can be seen in the felicity (linguistics)">infelicity of ''epistemic contradictions''.
:Epistemic contradiction: #It's raining and it might not be raining.
These sentences have been argued to be bona fide logical contradictions, unlike superficially similar examples such as Moore's paradox">Moore sentences, which can be given a pragmatics (linguistics)">pragmatic
Pragmatism is a philosophical movement.
Pragmatism or pragmatic may also refer to:
*Pragmaticism, Charles Sanders Peirce's post-1905 branch of philosophy
*Pragmatics, a subfield of linguistics and semiotics
*''Pragmatics'', an academic journal in ...
explanation.
:Epistemic contradiction principle: \varphi \land \Diamond \neg \varphi \models \bot
These sentences cannot be analysed as logical contradictions within purely intersective frameworks such as the relational semantics for modal logic. The Epistemic Contradiction Principle only holds on the class of Kripke frame, relational frames such that Rwv \Rightarrow (w=v) . However, such frames also validate an entailment from \Diamond \varphi to \varphi. Thus, accounting for the infelicity of epistemic contradictions within a classical semantics for modals would bring along the unwelcome prediction that "It might be raining" entails "It is raining". Update Semantics skirts this problem by providing a nonintersective denotation for modals. When given such a denotation, the formula \Diamond \neg \varphi can update input contexts differently depending on whether they already contain the information that \varphi provides. The most widely adopted semantic entry for modals in update semantics is the ''test semantics'' proposed by Frank Veltman
Frank or Franks may refer to:
People
* Frank (given name)
* Frank (surname)
* Franks (surname)
* Franks, a medieval Germanic people
* Frank, a term in the Muslim world for all western Europeans, particularly during the Crusades - see Farang
Curre ...
.
*The test semantics for modals: C Diamond \varphi = \begin
C & \text Cvarphi
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet.
In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voicele ...
\neq \varnothing \\
\varnothing & \text
\end
On this semantics, \Diamond \varphi tests whether the input context could be updated with \varphi without getting trivialized, i.e. without returning the empty set. If the input context passes the test, it remains unchanged. If it fails the test, the update trivializes the context by returning the empty set. This semantics can handle epistemic contradictions because no matter the input context, updating with \varphi will always output a context that fails the test imposed by \Diamond \neg \varphi .[For a complete derivation of the Epistemic Contradiction Principle within Update Semantics, see for instance Goldstein (2016), p. 13. This derivation crucially depends on a particular definition of entailment, as well as an intersective semantic entry for \neg and a treatment of \land as updating consecutively with the conjuncts in their linear order.]
See also
* Conversational scoreboard In linguistics and philosophy of language, the conversational scoreboard is a tuple which represents the discourse context at a given point in a conversation. The scoreboard is updated by each speech act performed by one of the interlocutors.
Mo ...
* Donkey anaphora
Donkey sentences are sentences that contain a pronoun with clear meaning (it is Bound variable pronoun, bound semantics, semantically) but whose syntax, syntactical role in the sentence poses challenges to Linguist, grammarians. Such sentences def ...
* Discourse representation theory
In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT inclu ...
* Formal semantics of programming languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax.
Semantics describes the processes a ...
* Hans Kamp
Johan Anthony Willem "Hans" Kamp (born 5 September 1940) is a Dutch philosopher and linguist, responsible for introducing discourse representation theory (DRT) in 1981.
Kamp was born in Den Burg. He received a Ph.D. in Philosophy from UCLA in 19 ...
* Import-Export
* Irene Heim
Irene Roswitha Heim (born in Munich, Germany, on October 30, 1954) is a linguist and a leading specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before moving to the Massachusetts Institute of Technology i ...
* Modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...
* Scope (formal semantics) In formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "''Paulina doesn't drink beer but she does drink wine''," the proposition that Paulina drinks beer occurs within the sco ...
Notes
External links
Dynamic Semantics, Stanford Encyclopedia of Philosophy
Dynamic Semantics Notes, Daniel Rothschild
Dynamic Semantics and Pragmatic Alternatives, ESSLLI 2017 Course Notes
{{Non-classical logic
Semantics
Logic
Philosophy of language
Non-classical logic
Systems of formal logic
Linguistic modality